1. Field
The present invention relates to a position control apparatus and a disk apparatus for preventing displacement of an object due to a disturbance, and more particularly, to a position control apparatus and a disk apparatus for preventing displacement due to an unknown disturbance frequency.
2. Description of the Related Art
In recent years, devices for performing position control on objects with high precision are widely used. For example, in a disk apparatus that performs recording and reproduction of data on a rotating storage medium (such as a disk medium) with a head, the head is positioned onto a desired track of the storage medium, and data is read from or written on the track. In such a disk apparatus as a magnetic disk apparatus or an optical disk apparatus, it is very important to accurately position a head onto a target track, so as to achieve higher recording density.
One of the factors that hinder the positioning is the decentering caused when the centers of concentric servo signals on a disk differ from the rotational center of the motor. To correct the decentering, a control method involving an observer has been suggested (see Japanese Patent (KOKAI) No. 3,460,795, for example).
The decentering leads to sinusoidal position fluctuations that are in synchronization with an integral multiple of the rotation frequency of the disk. By the above mentioned observer control method, such sinusoidal position fluctuations can be restrained, and accurate positioning on each target track can be performed. However, to perform such a decentering correction, the frequency to be corrected should be known in advance. For example, the frequency to be corrected should be an integral multiple of the rotation frequency, or should be equal to or twice as high as the rotation frequency.
The second factor that hinders the positioning is the vibrations transmitted from outside the disk apparatus. The vibrations may have various waveforms, but in the following, sinusoidal vibrations are explained. Besides, the above decentering correction control may be applied for the case with frequencies that are not integral multiples of the rotation frequency.
In the above conventional structure, the frequency of a disturbance is of a known value. However, external vibrations transmitted from outside are unknown at the stage of designing the control system, and the frequency cannot be known in advance. Therefore, it is necessary to detect unknown frequencies. As long as the frequencies can be detected, position fluctuations due to external vibrations can be prevented (by adaptively following the external vibrations) according to the control method as disclosed in Japanese Patent (KOKAI) No. 3,460,795.
FIG. 18 illustrates the structure of a conventional control system that detects a disturbance frequency, and suppresses a sinusoidal disturbance at a predetermined frequency, so as to perform position following control. As illustrated in FIG. 18, an arithmetic module 120 calculates the position error e between a target position r and the current position y, and a control module (Cn) 121 calculates a control amount Un. With this control amount Un, a plant 122 (such as a VCM of a disk apparatus) is driven. In a disk apparatus, servo signals from a magnetic head are demodulated, and the current position y of the plant 122 is calculated and is fed back to the arithmetic module 120.
An estimator 124 estimates the angular frequency (o of an external vibration, with the use of the position error e and an internal variable of a disturbance suppression compensator 123 (Cd). A compensation table 125 stores constants of the compensator 123 (Cd) for suppressing external oscillations at each frequency ω. The disturbance suppression compensator 123 (Cd) corrects the internal constant in accordance with a constant that is read from the compensation table 125 in accordance with the angular frequency ω of the estimator 124. In this manner, a disturbance suppression control amount Ud is calculated from the position error e. An addition module 126 adds the control amount Un and the disturbance suppression control amount Ud, and outputs the addition result to the plant 122.
As described above, according to a conventional method, the angular frequency (the disturbance frequency) ω is estimated, and the internal constant of the compensator Cd is corrected in accordance with the value of the angular frequency ω. In this manner, an optimum operation of the compensator Cd is maintained over a wide frequency range (see Japanese Patent Application Publication (KOKAI) No. 2007-004946, for example).
To adapt to unknown disturbance frequencies, the estimated angular frequency ω is corrected whenever necessary in the conventional estimation of the angular frequency ω. Therefore, the adaptive law is obtained through an analog control system in the following manner. The rotation vector of the compensator that compensates periodic disturbances is expressed by the following series of equations (1):z1=A·cos(ωt),z2=A·sin(ωt).  (1)
In the equations (1), z1 and z2 represent the X-axis component and the Y-axis component of the rotation vector.
The following equations (2) are obtained by temporally differentiating z1 and z2 of the equations (1) with respect to time. Here, ω is function of time.
                                                        ⅆ                              ⅆ                t                                      ⁢            z            ⁢                                                  ⁢            1                    =                                                    -                A                            ·                              sin                ⁡                                  (                                      ω                    ⁢                                                                                  ⁢                    t                                    )                                            ·                              (                                  ω                  +                                                            ω                      ′                                        ⁢                    t                                                  )                                      =                                          -                z                            ⁢                                                          ⁢                              2                ·                                  (                                      ω                    +                                                                  ω                        ′                                            ⁢                      t                                                        )                                                                    ,                                  ⁢                                            ⅆ                              ⅆ                t                                      ⁢            z            ⁢                                                  ⁢            2                    =                                    A              ·                              cos                ⁡                                  (                                      ω                    ⁢                                                                                  ⁢                    t                                    )                                            ·                              (                                  ω                  +                                                            ω                      ′                                        ⁢                    t                                                  )                                      =                          z              ⁢                                                          ⁢                              1                ·                                  (                                      ω                    +                                                                  ω                        ′                                            ⁢                      t                                                        )                                                                    ,        .                            (        2        )            
The angle of the rotation vector is the tangent of the sin component z1 and the cos component z2, and the angular frequency ω is the differential value of the angle. Accordingly, the angular frequency ω of the rotation vector is determined by the following equation (3):
                                                                                          ⅆ                  θ                                                  ⅆ                  t                                            =                                                ⅆ                                      ⅆ                    t                                                  ⁢                                  (                                      ω                    ⁢                                                                                  ⁢                    t                                    )                                                                                                        =                              ω                +                                                      ω                    ′                                    ⁢                  t                                                                                                        =                                                ⅆ                                      ⅆ                    t                                                  ⁢                                                      tan                                          -                      1                                                        ⁡                                      (                                                                  z                        ⁢                                                                                                  ⁢                        2                                                                    z                        ⁢                                                                                                  ⁢                        1                                                              )                                                                                                                          =                                                                                          z                      ⁢                                                                                          ⁢                      1                      ⁢                                                                                                    ⅆ                            z                                                    ⁢                                                                                                          ⁢                          2                                                                          ⅆ                          t                                                                                      -                                                                                                                        ⅆ                            z                                                    ⁢                                                                                                          ⁢                          1                                                                          ⅆ                          t                                                                    ⁢                      z                      ⁢                                                                                          ⁢                      2                                                                                                  z                      ⁢                                                                                          ⁢                                              1                        2                                                              +                                          z                      ⁢                                                                                          ⁢                                              2                        2                                                                                            .                                                                        (        3        )            
Here, the compensator uses the following equation (4) In the equation (4), ω is assumed to be a constant.
                              s          ⁡                      (                                                                                z                    ⁢                                                                                  ⁢                    1                                                                                                                    z                    ⁢                                                                                  ⁢                    2                                                                        )                          =                                            (                                                                    0                                                                              -                      ω                                                                                                            ω                                                        0                                                              )                        ⁢                          (                                                                                          z                      ⁢                                                                                          ⁢                      1                                                                                                                                  z                      ⁢                                                                                          ⁢                      2                                                                                  )                                +                                    (                                                                                          L                      ⁢                                                                                          ⁢                      4                                                                                                                                  L                      ⁢                                                                                          ⁢                      5                                                                                  )                        ⁢                          e              .                                                          (        4        )            
In the equation (4), z1 represents the sine component of the disturbance, z2 represents the cosine component of the disturbance, L4 and L5 represent input gains, e represents the position error, and s represents the Laplacian.
The state equation of the analog compensator of the equation (4) is expanded, and the differentials of z1 and z2 are determined. The following equation (5) is obtained by substituting the differentials of z1 and z2 into the equation (3)
                                                                        ω                +                                                      ω                    ′                                    ⁢                  t                                            =                                                                    z                    ⁢                                                                                  ⁢                    1                    ⁢                                          (                                                                                                    ω                            ·                            z                                                    ⁢                                                                                                          ⁢                          1                                                +                                                  L                          ⁢                                                                                                          ⁢                                                      5                            ·                            e                                                                                              )                                                        -                                                            (                                                                                                                                  -                              ω                                                        ·                            z                                                    ⁢                                                                                                          ⁢                          2                                                +                                                  L                          ⁢                                                                                                          ⁢                                                      4                            ·                            e                                                                                              )                                        ⁢                    z                    ⁢                                                                                  ⁢                    2                                                                                        z                    ⁢                                                                                  ⁢                                          1                      2                                                        +                                      z                    ⁢                                                                                  ⁢                                          2                      2                                                                                                                                              =                              ω                +                                                                                                    L                        ⁢                                                                                                  ⁢                                                  5                          ·                          z                                                ⁢                                                                                                  ⁢                        1                                            -                                              L                        ⁢                                                                                                  ⁢                                                  4                          ·                          z                                                ⁢                                                                                                  ⁢                        2                                                                                                            z                        ⁢                                                                                                  ⁢                                                  1                          2                                                                    +                                              z                        ⁢                                                                                                  ⁢                                                  2                          2                                                                                                      ⁢                                      e                    .                                                                                                          (        5        )            
If the estimated angular frequency of an unknown disturbance is correct, the compensator 123 (Cd) can properly suppress the disturbance. As a result, the position error e or the estimated position error of the observer becomes zero. In other words, when the angular frequency ω to be processed by the compensator 23 (Cd) is the same as the estimated angular frequency ω of a disturbance, ω′ of the equation (5) or the term of the position error e of the right side should be zero. Accordingly, the equation (5) is expressed by a time differential form of the angular frequency, to obtain the adaptive law (an integral compensation law) expressed by the following equation (6):
                                          ⅆ                          ⅆ              t                                ⁢          ω                =                              K            ·                                                            L                  ⁢                                                                          ⁢                                      5                    ·                    z                                    ⁢                                                                          ⁢                  1                                -                                  L                  ⁢                                                                          ⁢                                      4                    ·                    z                                    ⁢                                                                          ⁢                  2                                                                              z                  ⁢                                                                          ⁢                                      1                    2                                                  +                                  z                  ⁢                                                                          ⁢                                      2                    2                                                                                ⁢                      e            .                                              (        6        )            
The value of ω is corrected whenever necessary, with the use of this equation. The equation (6) is transformed into an integral form expressed by a digital control equation, and the following equation (7) is obtained:
                              ω          ⁡                      [                          k              +              1                        ]                          =                              ω            ⁡                          [              k              ]                                +                                    K              ·                                                                    L                    ⁢                                                                                  ⁢                                          5                      ·                      z                                        ⁢                                                                                  ⁢                                          1                      ⁡                                              [                        k                        ]                                                                              -                                      L                    ⁢                                                                                  ⁢                                          4                      ·                      z                                        ⁢                                                                                  ⁢                                          2                      ⁡                                              [                        k                        ]                                                                                                                                  z                    ⁢                                                                                  ⁢                                                                  1                        ⁡                                                  [                          k                          ]                                                                    2                                                        +                                      z                    ⁢                                                                                  ⁢                                                                  2                        ⁡                                                  [                          k                          ]                                                                    2                                                                                            ⁢                          e              .                                                          (        7        )            
Here, K represents the adaptive gain. The equation (7) uses the adaptive law in an addition formula. This can be expressed by a multiplication formula. With the use of this adaptive law, a linear relationship can be obtained between a disturbance oscillation frequency and the estimated frequency ω, as illustrated in FIG. 19.
In recent years, the aforementioned control system is applied to a digital control system so as to execute the above control system in data processing of a processor. In the above conventional technique, an analog adaptive law is obtained based on analog formulas, and the analog adaptive law is converted into a digital adaptive law. As a result, when the equation (7) is used in a digital control operation, a disturbance cannot be properly suppressed (or position following cannot be performed with respect to the disturbance) through digital disturbance adaptive control. This is because the estimated angular frequency ω is based on analog formulas, though it is directly determined.